1. Technical Field
The present invention is concerned with measuring a particle size distribution of a population of particles. Specifically, measuring a particle size distribution using a light scattering particle sizing instrument having a series of selectable imaginary component values of the refractive index.
2. Background Art
There are an ever-increasing number of organic compounds being formulated for therapeutic or diagnostic effects that are poorly soluble or insoluble in aqueous solutions. Such drugs provide challenges to delivering them by the administrative routes detailed above. Compounds that are insoluble in water can have significant benefits when formulated as a stable suspension of sub-micron particles. Accurate control of particle size is essential for safe and efficacious use of these formulations. Particles must be less than seven microns in diameter to safely pass through capillaries without causing emboli (Allen et al., 1987; Davis and Taube, 1978; Schroeder et al., 1978; Yokel et al., 1981). One solution to this problem is the production of small particles of the insoluble drug candidate and the creation of a microparticulate or nanoparticulate suspension. In this way, drugs that were previously unable to be formulated in an aqueous based system can be made suitable for intravenous administration. Suitability for intravenous administration includes small particle size (<7 μm), low toxicity (as from toxic formulation components or residual solvents), and bioavailability of the drug particles after administration.
Preparations of small particles of water insoluble drugs may also be suitable for oral, pulmonary, topical, ophthalmic, nasal, buccal, rectal, vaginal, transdermal administration, or other routes of administration. The small size of the particles improves the dissolution rate of the drug, and hence improving its bioavailability and potentially its toxicity profiles. When administered by these routes, it may be desirable to have particle size in the range of 5 to 100 μm, depending on the route of administration, formulation, solubility, and bioavailability of the drug. For example, for intravenous administration, it is desirable to have a particle size of less than about 7 μm. For pulmonary administration, the particles are preferably less than about 10 μm in size.
One common method to measure the particle size of these particles is image analysis using microscopy. However, existing image analysis methods can only provide a two-dimensional image (i.e., surface areas of the particles).
Another common method for particle size determination is to use a light scattering instrument, which measures the average particle size of a population of particles as well as the distribution of the particle size of the particles. The light scattering method reports a three-dimensional (i.e., volume) equivalent sphere diameter. One example of a commonly used light scattering instrument is the Horiba LA-920 laser light diffraction instrument. The light scattering method is particularly adapted to measuring particle size and particle size distributions of the small particles in a dispersion.
In order to measure the particle size and particle size distribution of these small particles by a light scattering instrument, two parameters are required for input into the instrument, the real component and the imaginary component of the refractive index of the particles, as expressed by the following equation:RI=n−ikwhere RI is the refractive index of the particles, n is the real component (also known as the real index) of the refractive index, which is the ratio of the velocity of light in a vacuum to the velocity of light in the particle, and k is the imaginary component (also known as the imaginary or complex index) of the refractive index, which is the extinction coefficient of the particle, and i=(−1)½. The imaginary component of the extinction coefficient k is the reduction of transmission of optical radiation in the particle caused by absorption and scattering of the light. It is expressed mathematically in the following equation:k=(λ/4π)αwhere α is the absorption coefficient and λ is the wavelength of light. The absorption coefficient (α) is the reciprocal of the distance that the light will penetrate the particle and be reduced to 1/e of its intensity before striking the particle. Transparent particles allow more penetration of light than opaque particles. Therefore, transparent particles have low absorption coefficient while opaque particles have high absorption coefficient.
The real and the imaginary components of the refractive index are further illustrated in FIGS. 1A and 1B. As shown in FIG. 1A, when a light beam strikes a particle, it is predominantly diffracted if the particle is large relative to the wavelength of the incident light (e.g. particle size of several microns and the wavelengths for Horiba LA-920 of 405 nm and 633 nm). Particle size index values are less significant in the measurement of size of these large particles. However, if the particles are small (e.g., submicron size) relative to the wavelength of the incident lights of, for example, 405 nm or 633 nm, the light can be absorbed and reradiated (FIG. 1B). The light striking the small particle is also scattered, mainly by refraction. In these small particles, the absorbed and reradiated light represents the imaginary component of the refractive index and the refracted light represents the real component of the refractive index (FIG. 1B). Particle size index values become very significant in the measurement of the size of these small particles.
The real component of the refractive index for a small particle can be measured using methods such as the Becke Line Method, or it can be obtained from published tables. However, there is no known method to measure the imaginary component portion of the refractive index for input into a light scattering particle sizing instrument. A value is selected by the user, for example, based on an estimate of the degree of transparency or opacity of the material being analyzed with one selectable imaginary component corresponding to completely opaque particles, another selectable imaginary component corresponding to translucent particles, another selectable imaginary component corresponding to particles that are most transparent but might have a rough surface or a non-spherical shape and another selectable imaginary component corresponding to transparent, spherical particles. For example, the options available for the refractive input on a laser light scattering instrument are 0.00i (completely transparent particles), 0.01i, 0.10i, and 1.0i (some what opaque to opaque particles). The manufacturer recommends that if the particles are not completely transparent or opaque, either 0.01i or 0.1i should probably be selected.
Additionally, light scattering particle sizing instruments calculate particle size and particle size distribution based on the assumption that all particles are spherical. The real components of the refractive index values are most important in particle size distribution measurements if the particles are (i) small, (ii) spherical, and (iii) transparent. If the characteristics of the particles deviate from any or all of these conditions, the real components of the refractive index are less important and the selection of higher imaginary components is recommended.
The imaginary component is most important when the size of the particles being measured is close to the wavelengths of the light source (e.g., the wavelengths for Horiba LA-920 are 405 nm and 633 nm), for example when measuring ultra-fine sub-micron particles (less than one micron). A need exists to accurately determine the selectable imaginary component of the refractive index for small sized particles.
The present invention discloses a method to determine the correct value of imaginary component of the particles which can be used to more accurately determine the particle size and particle size distribution, particularly the 100 percentile particle size distribution. The method is most applicable to particles of less than 1 μm.